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Definition df-oppg 15097
Description: Define an opposite group, which is the same as the original group but with addition written the other way around. df-oppr 15683 does the same thing for multiplication. (Contributed by Stefan O'Rear, 25-Aug-2015.)
Assertion
Ref Expression
df-oppg  |- oppg  =  ( w  e.  _V  |->  ( w sSet  <. ( +g  `  ndx ) , tpos  ( +g  `  w
) >. ) )

Detailed syntax breakdown of Definition df-oppg
StepHypRef Expression
1 coppg 15096 . 2  class oppg
2 vw . . 3  set  w
3 cvv 2916 . . 3  class  _V
42cv 1648 . . . 4  class  w
5 cnx 13421 . . . . . 6  class  ndx
6 cplusg 13484 . . . . . 6  class  +g
75, 6cfv 5413 . . . . 5  class  ( +g  ` 
ndx )
84, 6cfv 5413 . . . . . 6  class  ( +g  `  w )
98ctpos 6437 . . . . 5  class tpos  ( +g  `  w )
107, 9cop 3777 . . . 4  class  <. ( +g  `  ndx ) , tpos  ( +g  `  w
) >.
11 csts 13422 . . . 4  class sSet
124, 10, 11co 6040 . . 3  class  ( w sSet  <. ( +g  `  ndx ) , tpos  ( +g  `  w
) >. )
132, 3, 12cmpt 4226 . 2  class  ( w  e.  _V  |->  ( w sSet  <. ( +g  `  ndx ) , tpos  ( +g  `  w
) >. ) )
141, 13wceq 1649 1  wff oppg  =  ( w  e.  _V  |->  ( w sSet  <. ( +g  `  ndx ) , tpos  ( +g  `  w
) >. ) )
Colors of variables: wff set class
This definition is referenced by:  oppgval  15098
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